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13 votes
0 answers
615 views

The derived category of integral representations of a Dynkin quiver

Let $Q$ be a Dynkin quiver. Let $\mathbb CQ$ be its complex path algebra. It is defined in a way such that modules over $\mathbb CQ$ are the same as representations of the quiver $Q$. Let's write $\...
Rasmus's user avatar
  • 3,184
6 votes
0 answers
209 views

Classification of representation-finite algebras up to stable equivalence of Morita type

Assume $K$ is an algebraically closed field. I wanted to ask if there is a classification of the representation-finite $K$-algebras up to stable equivalence of Morita type (at least for some small ...
Mare's user avatar
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6 votes
0 answers
749 views

Tensor product of quivers

As a special case of a general construction I have constructed "accidentally" a tensor product of quivers aka directed multigraphs (aka directed graphs for category theorists). Probably this ...
Martin Brandenburg's user avatar
5 votes
0 answers
383 views

Kac's theorem for quiver representations over an arbitrary ground field

Let $Q$ be a quiver without loops (cycles of length 1). Kac proved that if $K$ is algebraically closed, the dimension vectors of indecomposable representations of $Q$ over $K$ are exactly the ...
Hugh Thomas's user avatar
  • 6,292
4 votes
0 answers
429 views

Auslander-Reiten-Quivers of representation-finite algebras having different 3-dimensional forms

I am looking for references, where I can find (pictures of) connected Auslander-Reiten-Quivers of representation-finite $k$-algebras ($k$ is a (preferably, but not necessarily finite) field) with one ...
Bernhard Boehmler's user avatar
3 votes
0 answers
679 views

Ext Quivers and their applications to Representation Theory

I am looking for references that provide an overview of the following two topics (it can be multiple references if necessary): How to compute the Ext-quiver of a (locally finite or finite) $\mathbb{C}...
Siddharth Venkatesh's user avatar
2 votes
0 answers
104 views

$G$-module representations of a profinite quiver

I have a profinite directed graph $\Gamma$, i.e., I can think of $\Gamma$ as the inverse limit of a directed system of finite directed graphs under inclusion. To each vertex of the graph a $G$-module ...
Qui's user avatar
  • 21
0 votes
0 answers
195 views

Automorphisms of weighted quiver

I am reading this paper strongly primitiv species with potentials I : mutations. In page 6, they give the definition of weighted quiver: a weighted quiver is a pair $(Q,d)$, where $Q$ is a loop-...
Xiaosong Peng's user avatar